Grover’s algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator inverts the sign on only one state. Here we provide an exac...

There has been significant interest recently in using complex quantum systems to create effective nonreciprocal dynamics. Proposals have been put forward for the realization of artificial magnetic fields for photons and phonons; experimental progress is fast making these proposals a reality. Much wo...

We obtain photon statistics by using a quantum jump approach tailored to a system in which one or two qubits are coupled to a one-dimensional waveguide. Photons confined in the waveguide have strong interference effects, which are shown to play a vital role in quantum jumps and photon statistics. Fo...

We present the NMR implementation of a scheme for selective and efficient quantum process tomography without ancilla. We generalize this scheme such that it can be implemented efficiently using only a set of measurements involving product operators. The method allows us to estimate any element of th...

We present a flexible scheme to realize non-artificial non-Markovian dynamics
of an electronic spin qubit, using a nitrogen-vacancy center in diamond where
the inherent nitrogen spin serves as a regulator of the dynamics. By changing
the population of the nitrogen spin, we show that we can smoothly tune the
non-Markovianity of the electron spin's dynamic. Furthermore, we examine the
decoherence dynamics induced by the spin bath to exclude other sources of
non-Markovianity. The amount of collected measurement data is kept at a minimum
by employing Bayesian data analysis. This allows for a precise quantification
of the parameters involved in the description of the dynamics and a prediction
of so far unobserved data points.

The positivity conditions of the relative entropy between two thermal
equilibrium states $\hat{\rho}_1$ and $\hat{\rho}_2$ are used to obtain upper
and lower bounds for the subtraction of their entropies, the Helmholtz
potential and the Gibbs potential of the two systems. These limits are
expressed in terms of the mean values of the Hamiltonians, number operator, and
temperature of the different systems. In particular, we discuss these limits
for molecules which can be represented in terms of the Franck--Condon
coefficients. We emphasize the case where the Hamiltonians belong to the same
system at two different times $t$ and $t'$. Finally, these bounds are obtained
for a general qubit system and for the harmonic oscillator with a time
dependent frequency at two different times.

Weak potential wells (or traps) in one and two dimensions, and the potential
wells slightly deeper than the critical ones in three dimensions, feature
shallow bound states with localization length much larger than the well radii.
We address a simple fundamental question of how many repulsively interacting
bosons can be localized by such traps. We find that under rather generic
conditions, for both weakly and strongly repulsive particles, in two and three
dimensions--but not in one-dimension!--the potential well can trap infinitely
many bosons. For example, even hard-core repulsive interactions do not prevent
this "trapping collapse" phenomenon from taking place. For the weakly
interacting/dilute regime, the effect can be revealed by the mean-field
argument, while in the case of strong correlations the evidence comes from
path-integral simulations. We also discuss the possibility of having a
transition between the infinite and finite number of trapped particles when
strong repulsive inter-particle correlations are increased.

We present and theoretically report the influence of a class of
near-parity-time-(PT-) symmetric potentials with spectral filtering parameter
$\alpha_2$ and nonlinear gain-loss coefficient $\beta_2$ on solitons in the
complex Ginzburg-Landau (CGL) equation. The potentials do not admit
entirely-real linear spectra any more due to the existence of coefficients
$\alpha_2$ or $\beta_2$. However, we find that most stable exact solitons can
exist in the second quadrant of the $(\alpha_2, \beta_2)$ space, including on
the corresponding axes. More intriguingly, the centrosymmetric two points in
the $(\alpha_2, \beta_2)$ space possess imaginary-axis (longitudinal-axis)
symmetric linear-stability spectra. Furthermore, an unstable nonlinear mode can
be excited to another stable nonlinear mode by the adiabatic change of
$\alpha_2$ and $\beta_2$. Other fascinating properties associated with the
exact solitons are also examined in detail, such as the interactions and energy
flux. These results are useful for the related experimental designs and
applications.

Strong correlation effects emerge from light-matter interactions in coupled
resonator arrays, such as the Mott-insulator to superfluid phase transition of
atom-photon excitations. We demonstrate that the quenched dynamics of a
finite-sized complex array of coupled resonators induces a first-order like
phase transition. The latter is accompanied by domain nucleation that can be
used to manipulate the photonic transport properties of the emerging superfluid
phase; this in turn leads to an empirical scaling law. This universal behavior
emerges from the light-matter interaction and the topology of the array. The
validity of our results over a wide range of complex architectures might lead
to to a promising device for use in scaled quantum simulations.

We present three classes of symmetric broadband composite pulse sequences.
The composite phases are given by analytic formulas (rational fractions of
$\pi$) valid for any number of constituent pulses. The transition probability
is expressed by simple analytic formulas and the order of pulse area error
compensation grows linearly with the number of pulses. Therefore, any desired
compensation order can be produced by an appropriate composite sequence; in
this sense, they are arbitrarily accurate. These composite pulses perform
equally well or better than previously published ones. Moreover, the current
sequences are more flexible as they allow total pulse areas of arbitrary
integer multiples of $\pi$.

Deffner and Lutz [J. Phys. A 46, 335302 (2013) and Phys. Rev. Lett. 111,
010402 (2013).] extended the Mandelstam-Tamm bound and the Margolus-Levitin
bound to time-dependent and non-Markovian systems, respectively. Although the
derivation of the Mandelstam-Tamm bound is correct, we point out that thier
analysis of the Margolus-Levitin bound is incorrect. The Margolus-Levitin bound
has not yet been established in time-dependent quantum systems, except for the
adiabatic case.

Fibonacci anyons are attractive for use in topological quantum computation
because any unitary transformation of their state space can be approximated
arbitrarily accurately by braiding. However there is no known braid that
entangles two qubits without leaving the space spanned by the two qubits. In
other words, there is no known "leakage-free" entangling gate made by braiding.
In this paper, we provide a remedy to this problem by supplementing braiding
with measurement operations in order to produce an exact controlled rotation
gate on two qubits.

The state spaces of both classical and quantum systems have a point-asymmetry
about the maximally mixed state except for bit and qubit systems. In this
paper, we find an informational origin of this asymmetry: In any operationally
valid probabilistic model, the state space has a point-asymmetry in order to
store more than a single bit of information. In particular, we introduce a
storable information as a natural measure of the storability of information and
show the quantitative relation with the so-called Minkowski measure of the
state space, which is an affinely invariant measure for point-asymmetry of a
convex body. We also show the relation between these quantities and the
dimension of the model, inducing some known results in \cite{ref:KNI} and
\cite{ref:FMPT} as its corollaries. Also shown are a generalization of weaker
form of the dual structure of quantum state spaces, and a generalization of the
maximally mixed states as points of the critical set.

We present a mathematical framework for quantum mechanics in which the basic
entities and operations have physical significance. In this framework the
primitive concepts are states and effects and the resulting mathematical
structure is a convex effect algebra. We characterize the convex effect
algebras that are classical and those that are quantum mechanical. The quantum
mechanical ones are those that can be represented on a complex Hilbert space.
We next introduce the sequential product of effects to form a convex sequential
effect algebra. This product makes it possible to study conditional
probabilities and expectations.

We investigate the qubit in the hierarchical environment where the first
level is just one lossy cavity while the second level is the N-coupled lossy
cavities. In the weak coupling regime between the qubit and the first level
environment, the dynamics crossovers from the original Markovian to the new
non-Markovian and from no-speedup to speedup can be realized by controlling the
hierarchical environment, i.e., manipulating the number of cavities or the
coupling strength between two nearest-neighbor cavities in the second level
environment. And we find that the coupling strength between two
nearest-neighbor cavities and the number of cavities in the second level
environment have the opposite effect on the non-Markovian dynamics and speedup
evolution of the qubit. In addition, in the case of strong coupling between the
qubit and the first level environment, we can be surprised to find that,
compared with the original non-Markovian dynamics, the added second level
environment cannot play a beneficial role on the speedup of the dynamics of the
system.

In this paper we investigate the completeness of the Stark resonant
eigenstates for a particle in a square-well potential. We find that the
resonant state expansions for target functions converge inside the potential
well and that the existence of this convergence does not depend on the depth of
the potential well. By analyzing the asymptotic form of the terms in these
expansions we prove some results on the relation between smoothness of target
functions and the rate of convergence of the corresponding resonant state
expansion.

We demonstrate the ability of an epitaxial semiconductor-superconductor
nanowire to serve as a field-effect switch to tune a superconducting cavity.
Two superconducting gatemon qubits are coupled to the cavity, which acts as a
quantum bus. Using a gate voltage to control the superconducting switch yields
up to a factor of 8 change in qubit-qubit coupling between the on and off
states without detrimental effect on qubit coherence. High-bandwidth operation
of the coupling switch on nanosecond timescales degrades qubit coherence.